@unnamedteam From their blog:
Fret not if you already have the Stack Exchange app
For now, the two apps have nearly identical functionality.
The new Stack Overflow app has one key difference: It only contains Stack Overflow questions and answers. The existing Stack Exchange app covers our network of more than 170 communities — including Stack Overflow. So, if you are a power user who actively participates in multiple Stack Exchange sites, you may want to keep it on your phone to continue seeing all of your Q&A in one place.
If you decide to download both apps, your notifications will be split between the two. Your Stack Overflow notifications will appear in the Stack Overflow app, and all other Stack Exchange notifications will appear in the Stack Exchange app.